In this appendix, I report additional exploratory factor analysis (EFA) results that were excluded from the main text of Chapter III, including: (a) unrotated versions of all of the EFA solutions reported in Chapter III; (b) oblimin-transformed (rather than varimax-rotated) versions of all of the EFA solutions reported in Chapter III; and (c) additional varimax-rotated EFA solutions not reported in full in Chapter III because I deemd to be redundant with the reported solutions.
Throughout this dissertation, beginning in Chapter III, I have reported EFA solutions after applying varimax rotation. This rotation, which maximizes the sum of the variances of the squared factor loadings, is intended to make factors more interpretable by producing “simple structure” (Thurstone, 1949). Here, for completeness, I present unrotated EFA solutions for all of the EFAs reported in Chapter III.
Throughout this dissertation, I have opted to focus on varimax-rotated EFA solutions, in which factors are constrained to be orthogonal (i.e., inter-factor correlations are 0). In my (admittedly anecdotal) experience, this rotation has tended to produce solutions that are more replicable when studies are repeated exactly, more similar across variants of the empirical approach, and easier to make factor retention decisions about. Orthogonal solutions also lend themselves more naturally to “scoring” individual participants on each of the underlying constructs because factors are, by definition, maximally distinct from one another. Since comparing EFA solutions across studies and age groups (Chapter III) and using these solutions to “score” participants on their assessments of the mental lives of different target characters (Chapter V) are two of the main goals of this dissertation, varimax rotations seemed to me to be appropriate for my current purposes.
However, “oblique” transformations, such as the “oblimin” transformation, also confer many advantages in using EFA to identify constructs of theoretical interest (for discussion, see Revelle, 2018, Chapter 6). In contrast to orthogonal rotations, oblique transformations allow factors to correlate with each other. In removing the orthgonality constraint, oblique transformations thus reveal relationships between variables (in my case, mental capacities) and factors (conceptual units) that might be considered more “natural”; they might also reveal new aspects of the relationships among factors themselves (pertinent to my goals in Chapter V).
In the interest of adding nuance to my primary discussions of the conceptual units identified by EFA (Chatper III) and the relationships among these units (Chapter V), here I present oblimin-transformed EFA solutions for all studies.
Different factor retention protocols suggested retaining between 3-5 factors for Studies 1a-1d. Here, I report 3-, 4-, and 5-factor solutions for all of these studies. When these factors seem similar to the BODY, HEART, and MIND factors presented in Chapter III, I have labeled them accordingly.
Here I present inter-factor correlations for all of the above EFA solutions for Studies 1a-1d.
Different factor retention protocols suggested retaining either 3 or 4 factors for adults in Study 2; all protocols suggested retaining 3 factors for children (ages 7-9y). Here, I report 3-, and 4-factor solutions for adults and the 3-factor solution for children. When these factors seem similar to the BODY, HEART, and MIND factors presented in Chapter III, I have labeled them accordingly.
Here I present inter-factor correlations for all of the above EFA solutions for Study 2.
Various factor retention protocols suggested retaining either 3 or 4 factors for adults in Study 3; 3 factors for older children (ages 7-9y); and either 1, 3, or 4 factors for younger children (ages 4-6y). Here, I report 3-, and 4-factor solutions for adults, the 3-factor solution for older children, and the 1-, 3-, and 4-factor solutions for younger children. When these factors seem similar to the BODY, HEART, and MIND factors presented in Chapter III, I have labeled them accordingly.